I would say there were several occations in with Arkansas Unionist and Arkansas Confederate fought each other. For example the capsule history of the 1st Arkansas Inf. U.S. taken from the Gerde's Website gives several oppertunities for such occations.

"The regiment’s active service began with duty at Fayetteville, Arkansas, where it assisted in repelling Cabell’s attack on Fayetteville on April 18, 1863. During the period April 25-May 4, 1863, it marched to Springfield, Missouri, and was stationed there until July 6, 1863, when it moved to Cassville, Missouri. On August 17, 1863, the First Arkansas joined the Army of the Frontier at Fort Gibson, Indian Territory. The regiment was engaged in the battle at Devil’s Back Bone (Back Bone Mountain) near Fort Smith, Arkansas, on September 1, 1863, then occupied Fort Smith, which had been in Confederate hands since the Spring of 1861. The First Arkansas was part of Steele’s expedition to Camden, March 23 to May 3, 1864, and fought at Prairie D’Ann, April 9-13; Moscow, April 13; and Jenkins’ Ferry on Saline River, April 30. At the conclusion of the expedition, the regiment returned to Fort Smith, where it was occupied with garrison duty, escort duty and duty on the frontier until August 10, 1865, when it mustered out of service."